Do I have to pay state tax for my resident state if I am a remote employee of a company in Texas?

Yes, if you actually performed the work in your resident state, that is considered income to that state regardless of where the company you work for is located.  

Even if you had physically worked in TX, you would owe tax to your home state. You report all your income on your resident state return, including the income earned in the other state. Your home state calculates tax on all your income, but gives you a credit, or partial credit, for tax you paid to the other state.

When you worked in a state without an income tax (e.g. Texas or Florida), there will be no credit, since there was no TX tax. In other words, having worked in a state without an income tax does not get you out of paying state tax on that income, to your home state.